This paper investigates the flow and heat transfer of special third-grade fluid with a viscous dissipation effect over a stretching sheet. This model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids domain. The governing momentum and energy equation are reduced to ordinary nonlinear differential (self-similar) equations via the Lie group transformation method. The Homotopy Perturbation Method (HPM) is applied to solve these obtaining results. For validation, current results have been compared with the fourth-order Runga method (RK4) and shooting technique. The effects of physical parameters on fluid velocity and temperature profile were investigated with the aid of figures and tables by simply altering a single parameter while keeping the others constant. It is observed that both the non-Newtonian parameter and the Prandtl number have the effect of decreasing the temperature of the stretching surface, while the opposite behavior was found for the Eckert number.

In this paper, the nonlinear Gardner-Kawahara (NLGK) equation has been investigated by using the Lie symmetry method. The symmetry method is applied to derive the infinitesimal generators and vector fields. The Lie symmetry method has reduced the nonlinear Gardner-Kawahara equation into a nonlinear ordinary differential equation form. In this article, we have obtained the exact solution of the NLGK equation in the explicit form by different significant methods. Further, the multiplier method has been used to derive the conservation laws of the nonlinear Gardner-Kawahara equation.

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